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Article

ZEMAX Simulations and Experimental Validation of Laser Interferometers

1
Department of Physics, Syed Babar Ali School of Science and Engineering, Lahore University of Management Sciences (LUMS), Lahore 54792, Pakistan
2
Extreme Light Infrastructure-Nuclear Physics (ELI-NP), ‘Horia Hulubei’ National Institute for R&D in Physics and Nuclear Engineering (IFIN-HH), 30 Reactorului Street, 077125 Magurele, Romania
*
Author to whom correspondence should be addressed.
Photonics 2025, 12(3), 206; https://doi.org/10.3390/photonics12030206
Submission received: 3 February 2025 / Revised: 21 February 2025 / Accepted: 26 February 2025 / Published: 27 February 2025
(This article belongs to the Special Issue Advances in Interferometric Optics and Applications)

Abstract

:
This study presents the design, simulation, and experimental validation of six fundamental laser interferometer types: Sagnac, Mach–Zehnder, Michelson, Twyman–Green, Fizeau, and Fabry–Pérot. Using ZEMAX OpticStudio in non-sequential mode with the physical optics propagation (POP) algorithm, the simulations provide detailed insights into the optical performance of these interferometers. A direct comparison is made between the simulated and experimental fringe patterns, coherent irradiance distributions, and phase plots, demonstrating strong agreement and validating the accuracy of computational modeling for interferometric analysis. The Mach–Zehnder and Michelson configurations exhibit high adaptability and measurement precision, while the Fabry–Pérot interferometer achieves superior spectral resolution. Twyman–Green interferometry proves particularly effective in mapping surface irregularities for optical testing. The results confirm the reliability of ZEMAX OpticStudio for high-precision optical system design and analysis. The novelty of this work lies in the comparative study between ZEMAX simulations and experimental interferometric results, particularly fringe patterns and phase distributions. This approach provides a clearer understanding of interferometer performance and enhances the accuracy of optical metrology, offering valuable insights for both theoretical modeling and practical applications.

1. Introduction

Laser interferometry, the foundation of precision metrology, strongly relies on the performance of its light source, which acts as both the signal origin and the measurement reference [1]. Interferometers are precise instruments that leverage the principles of wave interference to measure minute differences in optical path lengths, enabling applications across physics, engineering, and materials science. By splitting a beam of light into multiple paths and recombining them, an interferometer creates interference patterns that encode information about the relative phase difference between the paths. These patterns are highly sensitive to path length, wavelength, or refractive index changes, making interferometers ideal for distance measurement, surface profiling, and refractive index characterization [2]. Interferometry is frequently used due to its better traceability, broad dynamic range, high sensitivity, and resolution [3]. Modern geometric measuring techniques using interferometry can be categorized in several ways. The advantages of interferometry include increased precision, fast response, and non-intrusive measurement, making it widely applicable in diverse fields [4]. Most interferometers divide the light from a single source into two beams that travel in distinct optical channels and then recombine to generate interference; however, under certain conditions, even two incoherent sources can interfere [5]. Interferometers represent the highest-quality length-measuring tools available in analytical science, enabling nanoscale precision measurements of optical components.
Since the invention of the Michelson interferometer, various interferometric methods have been developed for measuring displacement, distance, surface profiles, and wavefront distortions. These methods generally fall into three categories: single-point interferometry for displacement and distance measurement, point-scanning profilometry, and full-field interferometry for surface characterization. Interferometry can also be categorized based on the type of optical components used, such as grating-based or laser-based interferometry [6]. Light sources in interferometry are classified based on their wavelength characteristics, including single-wavelength, multi-wavelength, frequency-swept, and white-light sources. Optical interferometry can be implemented using various configurations, including Michelson, Fizeau, Linnik, Twyman–Green, Mach–Zehnder, and Fabry–Pérot interferometers, each offering different advantages in terms of resolution, measurement range, and specific applications [7]. For instance, Michelson interferometers are widely used in spectrometry [8] and gravitational wave detection [9], while Fabry–Pérot interferometers excel in high-resolution spectroscopy. Advances in optical technologies have further expanded the capabilities of these interferometers, allowing their integration into compact systems for real-time analysis and even nanoscale measurements. This combination of precision, adaptability, and real-time capability has made interferometers indispensable in scientific research and industrial applications.
An astronomical interferometer, for example, comprises multiple telescopes that combine their signals to achieve resolutions comparable to a telescope with a diameter equal to the longest baseline between its components [10,11]. Current applications of optical interferometry include precise distance, displacement, and vibration measurements; optical system testing; gas flow and plasma diagnostics; surface topography analysis [12]; temperature, pressure, and electromagnetic field sensing [13]; rotation sensing [14]; high-resolution spectroscopy; and laser frequency measurements. Emerging applications include high-speed all-optical electronics and next-generation gravitational wave detection systems [4].
While previous studies have primarily focused on either the theoretical simulation of interferometers [15,16,17,18,19] or their experimental realization [20,21], limited research has been conducted on the direct comparative validation of simulated and experimental interferometric fringe patterns, coherent irradiance distributions, and phase plots. This work addresses this gap by systematically comparing ZEMAX OpticStudio simulations with experimentally obtained interferometric results for six fundamental interferometer types. To our knowledge, no prior study has conducted such a detailed comparative analysis between simulated and real-world interferometric fringe formation. By leveraging the physical optics propagation (POP) algorithm in non-sequential mode, this work provides deeper insights into the accuracy of computational modeling for interferometric analysis, bridging the gap between numerical simulations and experimental optical metrology. This comparative approach not only validates the effectiveness of ZEMAX OpticStudio for high-precision optical system design but also enhances the understanding of interferometric behavior across different configurations.
This article presents the design and simulation of different types of laser interferometers using ZEMAX OpticStudio [22,23,24]. Key optical metrics are analyzed, such as output fringe patterns (irradiance, coherent irradiance), 2D coherence plots, and density plots of the coherent phase. The simulated results and experimental measurements for all the developed interferometers show strong agreement, reinforcing the reliability of computational modeling for high-precision optical metrology. The design simulations were carried out in non-sequential mode [25] using the physical optics propagation (POP) algorithm [26,27], which effectively models diffraction and wave phenomena. Through this comparative study, this paper highlights the efficiency of ZEMAX-based simulations in evaluating and optimizing interferometric systems, offering valuable insights into their practical applications and configurations.

2. Simulations and Experimental Validations, Analysis, and Discussion

2.1. Physical Optics Propagation (POP)

The design simulations of the interferometers are carried out using ZEMAX OpticStudio (Ansys 2014) software. It includes two main analysis modes: geometrical ray tracing and physical optics propagation (POP) [28]. Physical optics propagation (POP) describes how light travels through various optical components within a system. It involves analyzing and simulating the interaction of light with elements such as lenses, mirrors, and prisms. Physical optics models optical systems by propagating wavefronts, representing the beam as a discretely sampled array. This array moves through free space, and at each optical surface, a transfer function is applied to account for beam transformation. In contrast, geometrical optics [29] models systems by tracing rays, which are normal to wavefronts of constant phase. While both rays and wavefronts can describe a beam, their propagation differs. Rays move in straight lines without interference, whereas wavefronts propagate with coherent self-interference. This distinction leads to different beam representations in free space and optical systems. Ray tracing is efficient, versatile, and widely used for optical modeling, but it cannot accurately describe diffraction and some wave-based effects. Wavefront-based modeling is essential for capturing these phenomena, ensuring a more comprehensive optical system analysis.
Geometric optics describes light paths based on reflection and refraction, focusing on image formation, location, and magnification without considering wave effects. In contrast, physical optics propagation (POP) models light propagation using Maxwell’s equations [30], incorporating interference and diffraction to better understand light behavior, especially in fine-detail regions. POP treats light as an electromagnetic wave, analyzing interference, diffraction, and polarization to account for its wave-like properties. Unlike geometric optics, which provide a simplified ray-based approach for macroscopic optical systems, physical optics consider wavefront distortions [31], offering insights into aberrations and their influence on image quality. By addressing wave interactions, physical optics provides a more detailed and accurate representation of light behavior, particularly at smaller scales where diffraction and interference become significant. In physical optics propagation (POP), the wavefront is represented as an array of points, with each point storing the beam’s complex amplitude information. Users can define the array’s dimensions, sampling, and aspect ratio. The Fresnel diffraction method [32] or the angular spectrum propagation algorithm is employed to propagate the beam between surfaces. OpticStudio selects the algorithm that ensures the highest numerical accuracy. These diffraction propagation techniques produce accurate results regardless of propagation distance, beam characteristics, or surface apertures, including user-defined apertures (UDAs). In summary, while geometric optics is effective for general optical system modeling, physical optics provides a more comprehensive perspective, essential for understanding intricate wave-based phenomena that impact optical performance.
Some of the most important analysis tools provided by ZEMAX to evaluate the performance of the optical system are the spot diagram, coherence irradiance, coherent phase, and density plots. These tools give a clear idea of the performance efficiency of the designed optical system. We adopted the physical optics propagation (POP) algorithm over geometrical ray tracing because geometrical ray tracing can only be used when diffraction limits are negligible.

2.2. Sagnac Interferometer

The Sagnac interferometer [33] is a highly precise optical device that measures angular velocity by exploiting the principles of interference and the Sagnac effect. It detects the phase shift difference between two counter-propagating light beams traveling within a rotating frame, which arises due to the differential optical path lengths caused by the rotation of the apparatus [21]. The ZEMAX-designed experimental setup, as illustrated in Figure 1a, consists of a coherent light source, a beam splitter to split the light into clockwise and counterclockwise propagating beams, mirrors to guide the beams along a closed-loop path, and a photodetector to capture the resulting interference pattern. The loop in the experiment had a radius of r = 0.5 m, and the light source operated at a wavelength of λ0 = 632.8 nm with FWHM = 6 nm and power = 2 mW. The angular velocity of the interferometer was set to ω = 10 rad/s. These parameters were used in both the experimental and simulation setups to validate the theoretical model. According to the Sagnac effect theoretical phase shift, Δϕ = 8π2r2ω/cλ0 = 1.04 rad as per the experimental data, which is consistent with the experimental observations and simulated results. The interference fringes recorded at the detector, as shown in Figure 1b,c, shifted in accordance with this value, demonstrating excellent agreement between the theoretical model, experimental data, and simulation output.
The same parameters were used in the simulation to calculate the interference pattern. The coherent irradiance [28] plot, shown in Figure 2a, demonstrates the intensity distribution at the detector, with peaks indicating constructive interference and troughs indicating destructive interference. The phase distribution, illustrated in Figure 2b, reveals periodic variation across the detector. Additionally, the phase density plot in Figure 2c provides a detailed visualization of the rotational sensitivity, further validating the results. The strong agreement between the calculated phase shift (Δϕ = 1.04 rad), simulated data, and experimental observations underscores the precision of the Sagnac interferometer. The interferometer’s sensitivity is proportional to the enclosed area of the light path, A = πr2. Increasing the loop size can further amplify the phase shift, making the system scalable for applications requiring extreme precision. A shorter wavelength increases sensitivity to rotation (larger phase shift). The Sagnac interferometer is a reliable and versatile tool for measuring angular velocity and rotational sensing in various scientific and industrial applications.

2.3. Mach–Zehnder Interferometer

The Mach–Zehnder interferometer (MZI) [34,35] is a versatile tool in optical science, renowned for its adaptability in phase measurement and beam manipulation. It operates by splitting a coherent light beam into two distinct paths using a beam splitter, directing the beams along separate arms, and then recombining them to produce interference patterns. This interference is analyzed to measure phase shifts, refractive index changes, or other optical properties. Unlike simpler designs, the Mach–Zehnder configuration allows for precise manipulation of individual arms [15,36]. The ZEMAX-designed experimental setup, illustrated in Figure 3a, includes a He-Ne laser operating at a wavelength of λ0 = 632.8 nm with FWHM = 6 nm and power = 2 mW, two beam splitters with a 1:1 reflection-to-transmission ratio, two plane mirrors, and two CCD detectors to record the interference patterns. The interferometer’s two arms are linear and spatially separated, allowing for the inclusion of large samples or additional optical elements. The detectors capture parallel interference fringes, which result from the uniform variation in optical path difference between the two arms.
The interference pattern is a direct result of the phase difference Δϕ between the two arms, calculated as Δϕ = 2πΔL/λ0 ≈ 49.65 rad, where the path difference ΔL = 5 μm. One of the mirrors is placed on a stage with a precise motor controller to produce an accurate path difference between the two arms. This phase difference corresponds to the fringe pattern observed in Figure 3b,c, alternating bright and dark lines representing constructive and destructive interference. ZEMAX simulation results provide additional insights into the behavior of the interferometer. The coherent irradiance plot in Figure 4a demonstrates the spatial intensity distribution, while the phase plot in Figure 4b highlights the linear phase variation across the detector. The phase density plot in Figure 4c emphasizes the interferometer’s sensitivity to minute phase changes, showcasing its ability to detect subtle variations in experimental conditions. These results strongly agree with the experimental observations, further validating the theoretical model.
Unlike the radial symmetry of the Michelson interferometer, the Mach–Zehnder interferometer’s parallel fringe pattern results from its linear optical path difference and spatially separated arms. This characteristic makes it suitable for fluid dynamics studies, wavefront distortion analysis, and material characterization applications. The agreement between the calculated phase difference (Δϕ ≈ 49.65 rad), simulated outputs, and experimental data confirms the precision and robustness of Mach–Zehnder’s ZEMAX-designed configuration.

2.4. Michelson Interferometer

The Michelson interferometer [37,38] is a foundational instrument in optics, renowned for its precision in detecting minute changes in optical path lengths. It operates by splitting a coherent light beam into two paths using a partially reflective mirror, directing each path to a different mirror, and recombining the reflected beams to produce an interference pattern. The resulting pattern depends on the relative phase difference between the two paths, which is influenced by variations in distance, refractive index, or wavelength. The ZEMAX-designed experimental setup, as illustrated in Figure 5a, includes a He-Ne laser operating at a 632.8 nm center wavelength (λ0) with 5 nm FWHM and 3 mW of power, two plane mirrors, a beam splitter with a 50:50 reflection-to-transmission ratio, and a detector. A plano-convex lens is used after the source in setups to adjust the beam waist of the incoming light. The beam splitter divides the incoming light beam into two equal-intensity beams that travel along separate arms, reflect off the mirrors, and recombine at the detector to form interference fringes. The choice of laser wavelength in interferometry depends on the trade-off between phase sensitivity, coherence length, and material properties. Shorter wavelengths provide higher resolution, while longer wavelengths enhance stability and penetration through certain materials. The optical path difference ΔL between the interferometer’s arms determines the interference pattern (ΔL = 2.5 μm). The phase difference Δϕ introduced by this path difference is Δϕ = 4πΔL/λ0 ≈ 49.65 rad.
This theoretical phase difference corresponds to the circular interference fringes observed experimentally, as shown in Figure 5b,c. These fringes form a “bull’s eye” pattern, with the center representing regions of equal optical path lengths in the two arms. Moving outward radially increases the path difference, producing concentric bright (constructive interference) and dark (destructive interference) rings. The symmetrical radial geometry arises due to the alignment of the mirrors and beam splitter, which creates a uniform optical system.
The ZEMAX simulation results depicted in Figure 6a–c further validates the theoretical model. The coherent irradiance plot shows the radial intensity distribution of the interference pattern, with peaks representing regions of constructive interference and troughs corresponding to destructive interference. The phase plot reveals the radial variation in phase, consistent with the symmetrical design of the Michelson interferometer. The phase density plot also emphasizes the interferometer’s sensitivity to minute phase changes, showcasing its capability to detect subtle variations in experimental conditions.
The experimental and simulated results exhibit remarkable agreement, with the calculated phase difference (Δϕ ≈ 49.65 rad) matching the observed fringe pattern 6(c). This consistency, further validated through ZEMAX simulations, highlights the Michelson interferometer’s precision and reliability and our simulation’s efficiency in accurately predicting its performance for applications requiring high sensitivity and accuracy.

2.5. Twyman–Green Interferometer

The Twyman–Green interferometer [39,40] is a modified version of the Michelson interferometer, specifically designed for precision testing of optical components and systems. It operates by splitting a collimated beam of monochromatic light into two paths, one directed toward the optical element under test and the other toward a reference mirror. When these beams are recombined, the resulting interference pattern provides detailed information about the optical quality of the tested surface, including surface irregularities, wavefront distortions, and alignment errors. The ZEMAX-designed experimental setup, illustrated in Figure 7a, integrates a He-Ne laser operating at a wavelength of λ0 = 632.8 nm with FWHM = 6 nm, a test optical component (e.g., a plane mirror), a reference mirror, and a detector. The ZEMAX design highlights the system’s precision, accurately representing the light paths and their interactions.
The interference fringes observed in the Twyman–Green interferometer arise due to phase differences between the test wavefront and the reference wavefront. The phase difference Δϕ is calculated using the equation Δϕ = 4πΔL/λ0; for this setup, an optical path difference of ΔL = 1.5 μm, and the phase difference Δϕ ≈ 29.79 rad. This theoretical phase difference matches the experimental interference fringes observed in Figure 7b,c, confirming the accuracy of the optical design and setup.
The observed “fingerprint” fringe pattern in the Twyman–Green interferometer results from localized phase distortions introduced by the test optical component. If the test surface deviates from an ideal plane or sphere, it introduces phase variations superimposed with the reference wavefront, resulting in non-uniform fringes. These fringes directly map the surface deviations of the tested optical element. For instance, spherical aberrations produce concentric or quasi-concentric fringes, while astigmatism or tilt results in asymmetrically curved patterns. The spacing or width of the fringe provides additional information about the wavefront. The fringe width w is given by w = λ0/θ is the angular difference in the wavefronts. For an angular variation of θ = 0.01 rad, the fringe width is calculated as w = 63.28 μm. This narrow fringe width demonstrates the instrument’s capability to resolve sub-wavelength variations, critical for high-precision testing.
Simulated results, as shown in Figure 8a,b, further validate the system’s performance. The irradiance plot illustrates the intensity distribution of the fringes, with peaks corresponding to constructive interference and troughs representing destructive interference. The phase plot highlights variations in phase across the wavefront, mapping the localized deviations in the test optical surface. The phase density plot in Figure 8c not only emphasizes the interferometer’s sensitivity in detecting sub-wavelength surface irregularities but also validates the accuracy and efficiency of our simulation. The ZEMAX-based predictions align closely with experimental results, confirming our modeling approach’s robustness in capturing the Twyman–Green interferometer’s intricate optical behavior.

2.6. Fizeau Interferometer

The Fizeau interferometer [8,41] is a highly effective optical instrument widely used for precision measurements of surface flatness, thickness variations, and refractive index changes. It exploits the interference patterns generated by light waves reflected from two closely spaced surfaces. Its straightforward design includes a light source, a reference surface, and a test surface, allowing it to provide rapid and accurate measurements suitable for laboratory and industrial applications. When collimated light from the source strikes the reference and test surfaces, part of the light reflects back from each, and the superposition of these reflected beams creates an interference pattern. This pattern reveals the test surface’s flatness, separation, or curvature. The ZEMAX design of the Fizeau interferometer, as shown in Figure 9a, includes a BK7 glass test surface tilted slightly with respect to the transmission axis. The experimental and simulated interference patterns in Figure 9b,c exhibit strong agreement, validating the setup and confirming the effectiveness of the interferometer in high-precision surface measurements.
The interference fringes in a Fizeau interferometer correspond to variations in the air gap thickness d between the reference and test surfaces. The optical path difference (OPD) between the light beams reflected from these surfaces is given by OPD = 2dcos(θ), where d is the gap thickness, and θ is the light’s incidence angle for small angles (cos(θ) ≈ 1); the OPD simplifies to OPD ≈ 2d. Constructive interference (bright fringes) occurs when the OPD satisfies the condition 2d = mλ0, where m is the fringe order (an integer), and λ0 is the wavelength of the light source. For a He-Ne laser λ0 = 632.8 nm with FWHM = 5 nm and power = 3 mW, a gap thickness of d = 1.0 μm corresponds to an OPD of OPD = 2d = 2 × 1.0 μm = 2.0 μm. This satisfies the condition for constructive interference at m = OPD/λ0 ≈ 3, which corresponds to the third-order fringe.
The fringe width w depends on the angular variation of the air gap thickness and is given by w = λ0/Δθ, where Δθ is the angular change across a fringe. If Δθ = 0.01 rad, the fringe width is w = 63.28 μm. This narrow fringe spacing highlights the interferometer’s ability to resolve sub-wavelength surface deviations. The circularly symmetric fringes observed in Figure 9b arise because the air gap thickness varies radially. The gap increases uniformly from the center outward, producing concentric rings for a flat reference surface and a slightly curved test surface. A perfectly flat test surface against a flat reference surface would result in uniform spacing or no fringes if the surfaces were in perfect contact.
Simulated results, shown in Figure 10a,b provide further insights into the optical behavior of the interferometer. The coherent irradiance plot reveals the intensity distribution corresponding to the interference fringes, while the phase plot maps the wavefront distortions introduced by the test surface. The phase density plot in Figure 10c not only emphasizes the interferometer’s sensitivity to surface deviations but also highlights the efficiency and effectiveness of our simulation in accurately predicting sub-wavelength irregularities. The strong agreement between the simulated and expected results confirms the robustness of our modeling approach in capturing intricate optical behaviors with high precision.

2.7. Fabry–Pérot Interferometer

The Fabry–Pérot interferometer [42] is an essential optical device used to study the spectral characteristics of light with exceptional resolution. It operates by utilizing multiple reflections of light between two closely spaced, highly reflective surfaces to generate interference patterns. These patterns are characterized by sharp and evenly spaced transmission or reflection peaks, enabling precise analysis of the spectral composition of light sources, including lasers, atomic emissions, and molecular spectra. The device comprises two parallel mirrors, a coherent light source, and a detector. Light entering the cavity reflects multiple times between the mirrors, creating beams with varying optical path differences (OPDs) that interfere constructively or destructively. The condition for constructive interference is expressed as 2dcosθ = mλ, where d is the separation between the mirrors, θ is the angle of incidence, m is the interference order (integer), and λ is the wavelength of the light source. For a Fabry–Pérot cavity with d = 5.0 μm, λ = 532 nm, FWHM = 1 nm, and power = 10 mW at normal incidence (θ = 0), the interference condition simplifies to 2d = mλ. Substituting the values m ≈ 18.7, indicating that the observed fringes correspond to the 15th-order interference [43].
The Fabry–Pérot interferometer produces circular concentric fringes due to the OPD variation across the detector’s incidence angle. The fringe width or spacing is determined by the finesse () of the system, which quantifies the sharpness of the fringes. The finesse is = π(R)1/2/1−R, where R is the reflectivity of the mirrors. For R = 0.95 (95% reflectivity), ≈ 61.2. The fringe width w is then calculated as w = Δλ/, where Δλ = 0.1 nm represents the spectral resolution of the system. By substituting w ≈ 1.68 × 10−3 nm, this extremely narrow fringe width highlights the interferometer’s ability to accurately resolve closely spaced spectral lines.
The ZEMAX design experimental setup, illustrated in Figure 11a, consists of two parallel mirrors aligned to form a cavity structure. The ZEMAX schematic provides a detailed visualization of the optical layout, emphasizing the parallel alignment of the mirrors and the multiple reflections within the cavity. Simulated and experimental fringe patterns, as shown in Figure 11b,c, exhibit a remarkable degree of agreement. Both patterns feature sharp, evenly spaced concentric circular fringes, confirming the precision of the Fabry–Pérot design. The irradiance plot in Figure 11d reveals sharp intensity peaks corresponding to the transmission fringes, while the phase plot in Figure 11e demonstrates precise phase transitions within the cavity.
Some key characteristics of different laser interferometers are given in Table 1. The simulation closely reproduces the characteristics observed in the experimental results. The simulated fringes accurately mimic the sharpness, spacing, and symmetry of the experimental patterns, validating the theoretical model and the high finesse of the system. The circular symmetry in both simulation and experiment arises due to the uniform variation in OPD across the detector, ensuring that the results are consistent with the constructive interference condition. Additionally, the irradiance and phase plots highlight the system’s sensitivity to subtle wavelength changes, further reinforcing the reliability of the simulation in predicting experimental behavior.

3. Conclusions

This study underscores the power of ZEMAX OpticStudio simulations in unveiling and accurately predicting the performance of fundamental laser interferometers validated through experimental measurements. The simulations have provided deeper insights into their distinct operational characteristics by systematically analyzing six interferometer configurations: Sagnac, Mach–Zehnder, Michelson, Twyman–Green, Fizeau, and Fabry–Pérot. The strong agreement between simulated fringe patterns and experimental results confirms the reliability and precision of our modeling approach in replicating real-world interferometric behavior. The simulations reveal that Sagnac interferometers excel in rotational measurements, while Mach–Zehnder and Michelson’s configurations demonstrate exceptional versatility and precision. Twyman–Green and Fizeau interferometers are highly effective in optical testing applications, with Fabry–Pérot standing out for its superior spectral resolution. These findings highlight the critical role of simulation in elucidating the fundamental properties of interferometers, allowing for a more comprehensive understanding of their capabilities and limitations. By leveraging ZEMAX-based computational modeling, we minimize the need for extensive experimental iterations, improving design efficiency and optimizing interferometric system performance. This work reinforces the integration of simulation-driven methodologies in optical engineering, paving the way for more precise and efficient interferometric applications in scientific and industrial domains.

Author Contributions

Conceptualization, M.N. and T.I.; methodology, M.N. and T.I.; software, M.N. and T.I.; validation, M.N. and T.I.; formal analysis, M.N.; investigation, M.N.; resources, M.N. and T.I.; data curation, M.N.; writing—original draft preparation, M.N. and T.I.; writing—review and editing, M.N. and T.I.; visualization, M.N. and T.I.; supervision, T.I.; project administration, M.N. and T.I. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data supporting this manuscript’s findings is not available in any repository. The data supporting this study’s findings are available within the article.

Acknowledgments

The authors would like to greatly acknowledge the support of Muhammad Sabieh Anwar at Syed Babar Ali School of Science and Engineering, Lahore University of Management Sciences (LUMS), Lahore, Pakistan.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. (a) ZEMAX design of the Sagnac interferometer. (b) Simulated and (c) experimental output interference pattern at the detector. (BS = beam splitter).
Figure 1. (a) ZEMAX design of the Sagnac interferometer. (b) Simulated and (c) experimental output interference pattern at the detector. (BS = beam splitter).
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Figure 2. Simulated 2D (a) coherent irradiance and (b) coherent phase at the detector. (c) Simulated coherent phase density plot at the detector.
Figure 2. Simulated 2D (a) coherent irradiance and (b) coherent phase at the detector. (c) Simulated coherent phase density plot at the detector.
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Figure 3. (a) ZEMAX design of the Mach–Zehnder interferometer. (b) Simulated and (c) experimental output interference pattern at the detector. (BS = beam splitter).
Figure 3. (a) ZEMAX design of the Mach–Zehnder interferometer. (b) Simulated and (c) experimental output interference pattern at the detector. (BS = beam splitter).
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Figure 4. Simulated 2D (a) coherent irradiance and (b) coherent phase at the detector. (c) Simulated coherent phase density plot at the detector.
Figure 4. Simulated 2D (a) coherent irradiance and (b) coherent phase at the detector. (c) Simulated coherent phase density plot at the detector.
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Figure 5. (a) ZEMAX design of the Michelson interferometer. (b) Simulated and (c) experimental output interference pattern at the detector. (BS = beam splitter).
Figure 5. (a) ZEMAX design of the Michelson interferometer. (b) Simulated and (c) experimental output interference pattern at the detector. (BS = beam splitter).
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Figure 6. Simulated 2D (a) coherent irradiance and (b) coherent phase at the detector. (c) Simulated coherent phase density plot at the detector.
Figure 6. Simulated 2D (a) coherent irradiance and (b) coherent phase at the detector. (c) Simulated coherent phase density plot at the detector.
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Figure 7. (a) ZEMAX design of the Twyman–Green interferometer. (b) Simulated and (c) experimental output interference pattern at the detector. (BS = beam splitter, PM = plane mirror, SM = spherical mirror).
Figure 7. (a) ZEMAX design of the Twyman–Green interferometer. (b) Simulated and (c) experimental output interference pattern at the detector. (BS = beam splitter, PM = plane mirror, SM = spherical mirror).
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Figure 8. Simulated 2D (a) coherent irradiance and (b) coherent phase at the detector. (c) Simulated coherent phase density plot at the detector.
Figure 8. Simulated 2D (a) coherent irradiance and (b) coherent phase at the detector. (c) Simulated coherent phase density plot at the detector.
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Figure 9. (a) ZEMAX design of the Fizeau interferometer. (b) Simulated and (c) experimental output interference pattern at the detector. (BS = beam splitter).
Figure 9. (a) ZEMAX design of the Fizeau interferometer. (b) Simulated and (c) experimental output interference pattern at the detector. (BS = beam splitter).
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Figure 10. Simulated 2D (a) coherent irradiance and (b) coherent phase at the detector. (c) Simulated coherent phase density plot at the detector.
Figure 10. Simulated 2D (a) coherent irradiance and (b) coherent phase at the detector. (c) Simulated coherent phase density plot at the detector.
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Figure 11. (a) ZEMAX design of the Fabry–Pérot interferometer. (b) Experimental and (c) simulated output fringe pattern. Simulated (d) coherent irradiance and (e) coherence phase at the detector.
Figure 11. (a) ZEMAX design of the Fabry–Pérot interferometer. (b) Experimental and (c) simulated output fringe pattern. Simulated (d) coherent irradiance and (e) coherence phase at the detector.
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Table 1. Comparison of laser interferometer’s characteristics.
Table 1. Comparison of laser interferometer’s characteristics.
InterferometerKey FeaturesAdvantagesDisadvantagesApplications
SagnacSensitive to rotation (Sagnac effect)High sensitivity to rotationRequires precise alignment and stabilityGyroscopes, rotation sensing
Twyman–GreenUses a point source and collimating opticsHigh precision in optical surface measurementSensitive to vibrations and misalignmentOptical testing, metrology
Mach–ZehnderIndependent control of both armsFlexible design with separate pathsComplex alignment and stability issuesFlow visualization, quantum optics, refractive index measurements
MichelsonPath difference leads to interference fringesHigh precision in measuring small changesSensitive to environmental noiseLength measurement, gravitational wave detection (LIGO)
FizeauUsed for surface testing and thickness measurementHigh sensitivity to surface deviationsRequires highly controlled surfacesOptical flatness testing, film thickness measurement
Fabry–PérotProduces sharp interference fringesHigh finesse and wavelength selectivityRequires precise mirror spacing and alignmentHigh-resolution spectroscopy, laser cavity design
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Naeem, M.; Imran, T. ZEMAX Simulations and Experimental Validation of Laser Interferometers. Photonics 2025, 12, 206. https://doi.org/10.3390/photonics12030206

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Naeem M, Imran T. ZEMAX Simulations and Experimental Validation of Laser Interferometers. Photonics. 2025; 12(3):206. https://doi.org/10.3390/photonics12030206

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Naeem, Muddasir, and Tayyab Imran. 2025. "ZEMAX Simulations and Experimental Validation of Laser Interferometers" Photonics 12, no. 3: 206. https://doi.org/10.3390/photonics12030206

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Naeem, M., & Imran, T. (2025). ZEMAX Simulations and Experimental Validation of Laser Interferometers. Photonics, 12(3), 206. https://doi.org/10.3390/photonics12030206

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